The spin-orbit interaction energy refers to the interaction between the intrinsic angular momentum (spin) of a particle and its orbital angular momentum as it moves in a potential field, typically in the context of quantum mechanics.

In an atomic context, such as in the hydrogen atom, the spin-orbit interaction leads to splitting of spectral lines. For non penetrating orbit, the spin orbit interaction energy is similar to hydrogen like atom. Therefore spin orbit interaction energy in term of term value for hydrogen like orbit is given by

For any given doublet l and s have same value where j have two value j = l + 1/2 for upper level and j = l - 1/2 for lower level.

The term value for doublet j = l + 1/2 is

And the term value for the doublet j = l- 1/2 is

Term shift for non penetrating is

Introducing screening effect in case of non penetrating orbit, we get

Equation 5 is the required expression for the doublet separation in case of non penetrating orbit.

For a non-penetrating orbit, the electron spends most of its time away from the nucleus. Thus, the potential term V can be approximated as the electrostatic potential due to the nucleus.

However, the exact calculation might be quite complex and typically requires computational methods due to the involvement of quantum mechanics.

This note is a part of the Physics Repository.

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